question lesson goals€¦ · lesson goals apply the formula for the volume of a cone. calculate...
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© Edgenuity, Inc. 1
Warm-Up Applications with the Volume of a Cone
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WK2
Lesson Question
Words to Know
Fill in this table as you work through the lesson. You may also use the glossary to help you.
substitute to take the place of; to
cone a solid object with a base and one vertex
radius a that extends from the center of a circle to
any point on the circle
volumethe measure of the amount of space occupied by a
solid object
Lesson Goals
Apply the formula for the volume of a cone.
Calculate missing measures of
.Solve real-world .
the
© Edgenuity, Inc. 2
Instruction
2Slide
Applications with the Volume of a Cone
Calculating the Area of a Base
PROCEDURE
• Apply the for the
volume of a cone.
• Substitute the values for the
corresponding in the formula.
• Solve for the unknown variable.
What is the area of the base of a cone with a volume of 60 in.3 and a height of 9 in.?
13( )
1
3
60
609
3
B
V Bh
B
=
=
=
60 =
= B
The area of the base of the cone is equal to 20 in.2.
© Edgenuity, Inc. 3
Instruction Applications with the Volume of a Cone
5Slide
Calculating the Radius of a Cone
EXAMPLE
The volume of a cone with a height of 4 cm is 12π cubic centimeters. What is the radius of the base?
Cone 1
3V Bh=
= π
= π
π = π
13
( )
1
3
124
3
2
2
2
r
V r h
r
π
( )
π =
π
= ππ
=
=
r
r
r
r
3
412
3
4
4
3
9
2
2
2
3 = r
Let’s check the answer with substitution.
π
π
= π
π =
π =
π = π
V r h
13( )(4)
13( )
1
3
12
12
12 12
2
r = cm
© Edgenuity, Inc. 4
Instruction Applications with the Volume of a Cone
8Slide
Applying the Formula to a Real-World Scenario
REAL-WORLD CONNECTION
How much wax does it take to create a 9-inch tall conical candle with a 6-inch diameter base?
• Apply the formula for the volume
of a .
• Substitute the values for the corresponding variables in the formula.
• Solve for the unknown variable.
Cone 1
3V Bh=
=
= π
V
V1
3(3) (9)2
V
V
V
V
π
= π
=
= π
= π
13( )
1
3(9)(9)
81
3
27
V ≈ in.3
The amount of wax it will take to create the cone is approximately 84.8 in.3.
© Edgenuity, Inc. 5
Instruction Applications with the Volume of a Cone
Slide
Solving a Real-World Problem
EXAMPLE
Chloe was given a gift of a conical bird feeder that has a volume of 785.4 cubic centimeters and a height of 18 centimeters. What is the area of the lid she will need to cover the feeder?
=
=
=
B
V Bh
B
13( )
1
3
785.4
6
6
6
cm2 = B
So the base of the lid that she’ll need to cover the feeder is 130.9 cm2.
Solve a Real-World Problem Using the Volume
EXAMPLE
Chloe was given a gift of a conical bird feeder that has a volume of 785.4 cubic centimeters. Bird seed is sold in packages of 100 cubic centimeters for $2.25 per package. How much will Chloe pay to fill the empty bird feeder?
V ≈ cm3
800
100= packages
8( ) = 18$ to fill the feeder.
10
13
© Edgenuity, Inc. 6
Summary Applications with the Volume of a Cone
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Answer
Lesson Question
How can you use the formula for the volume of a cone to solve problems?
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